R.J.
Yep.
My son got violently ill from gentle ease formula.
Other kids will get violently ill from your baby's perfect formula.
SOMETIMES you can transition babies by mixing 25/75, 50/50, 75/25... But most of the time, not. Formulas are all different (same nutrition, different ways of getting there)... Because babies react differently to them (projectile vomiting, reflux, gas, constipation, sleep issues).
In order for WIC to change your formula type... You have to go through a doctor who can document their reaction to the formula.
Even then, it depends on your local WIC office on whether or not they'll do a brand change or ONLY do 1 brand + Nutrimigen (and that's a major pain to get from WIC, but they will).
What many moms I know do... They get the WIC formula, and then exchange it for the brand that doesn't make their babies sick. Formula is tricky to exchange (it usually cannot leave the store), so you'll need to work with the store to be able to do so AHEAD of time. There's also usually a price difference (couple dollars).
In the meantime... Take your baby to the doctor.
It starts the documentation process, and your led will usually have samples of formula... So you can switch back, or start mixing. And then make an appt with your WIC office, to find out if they'll work with you on brand/type or if you need to work outside they system.